A R is true
B R is false
C R is unknown
D Q is false
Explanation: By chaining modus ponens, if P→Q and Q→R and P is true, then Q is true and R is true.
A Vehicle X is a car
B Vehicle X might be a car
C Vehicle X is not a car
D All fuel-needing things are cars
Explanation: Needing fuel doesn\'t prove Vehicle X is a car; trucks and motorcycles also need fuel.
A Taxes affect businesses
B Small businesses don\'t always create jobs when taxes are cut
C Job creation is good
D Tax cuts are popular
Explanation: If tax cuts don\'t always lead to job creation, the conclusion doesn\'t necessarily follow.
A Contradiction
B B is true from another cause
C A is true
D Both are true
Explanation: If A is necessary for B and A is false, B cannot be true. This is a contradiction.
A All fruits are acidic
B Some fruits are acidic
C No fruits are acidic
D All acidic things are citrus
Explanation: Since some fruits are citrus and all citrus fruits are acidic, some fruits are acidic.
A A logical argument
B An ad hominem attack
C A valid criticism
D A fact
Explanation: Dismissing a law based on who passed it is an ad hominem attack.
A A is true
B A is false
C A is unknown
D B is false
Explanation: D being true doesn\'t prove A is true; the chain of implications can be triggered by other causes.
A Document Z is a book
B Document Z might be a book
C Document Z is not a book
D All paged things are books
Explanation: Having pages doesn\'t prove Document Z is a book; newspapers and magazines also have pages.
A Exercise is popular
B Self-reported stress indicates actual stress
C Stress is bad
D Exercise is healthy
Explanation: If self-reported stress indicates actual stress, this strengthens the claim about exercise and stress.
A A is false
B A is true
C Both are false
D Both are true
Explanation: If A and B cover all possibilities and B is false, A must be true.
A All students are fit
B Some students are fit
C No students are fit
D All fit people are athletes
Explanation: Since some students are athletes and all athletes are fit, some students are fit.
A Critical thinking
B A fallacy of consensus
C A logical argument
D A fact
Explanation: Dismissing science because of disagreement is a fallacy; disagreement is part of the scientific process.
A Contradiction
B Q is true from another cause
C P is true
D P is unknown
Explanation: P being false while Q is true means Q came from another cause, not P.
A Plant B is an animal
B Plant B is not an animal
C Plant B might be an animal
D All food-needing things are animals
Explanation: If Plant B doesn\'t need food, it cannot be an animal since all animals need food.
A Education funding affects quality
B Prosperity is desirable
C Education creates prosperity
D All of the above
Explanation: The argument requires all these assumptions for the conclusion to be valid.
A B is true
B B is false
C B is unknown
D A is false
Explanation: If A and B are equivalent and A is true, B must be true.
A All fruits grow on trees
B Some fruits grow on trees
C No fruits grow on trees
D All tree-grown things are fruits
Explanation: Since some fruits are apples and all apples grow on trees, some fruits grow on trees.
A A fact
B An age-based stereotype
C A logical conclusion
D A proven claim
Explanation: Assuming old age equals wisdom is an age-based stereotype.
A Nothing new follows
B B is false
C A is false
D Both are false
Explanation: If both necessary condition and result are true, this is consistent but nothing new follows.
A Flower Y is a rose
B Flower Y might be a rose
C Flower Y is not a rose
D All sunlight-needing things are roses
Explanation: Needing sunlight doesn\'t tell us what type of flower Y is.